A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.
An unsuitable alignment between transmitter and receiver together with fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence can severely degrade the performance of free-space optical (FSO) systems. In this paper, cooperative FSO communications with decode-and-forward (DF) relaying and equal gain combining (EGC) reception over atmospheric turbulence and misalignment fading channels is analyzed in order to mitigate these impairments. Novel closed-form asymptotic bit error-rate (BER) expressions are derived for a 3-way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), following a gamma-gamma distribution of parameters α and β , or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2β 1/2 times the value of the pointing error displacement standard deviation at the receiver. It is contrasted that the available diversity order is strongly dependent on the relay location, achieving greater diversity gains when the diversity order is determined by β AC + β BC , where β AC and β BC are parameters corresponding to the turbulence of the source-destination and relay-destination links. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results. site," URL http://functions.wolfram.com. 36. V. S. Adamchik and O. I. Marichev, "The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system," in Proc. Int. Conf. on Symbolic and Algebraic Computation, 212-224 (Tokyo, Japan, 1990).
Despite the fact that underwater optical wireless communication (UOWC) systems are able to provide high-data rate links with high security, the performance of these systems presents several limitations related to the maximum achievable distance due to attenuation, and scattering effects. Hence, quantifying the signal attenuation, and the time-dispersion produced by such effects represents a crucial work in channel modeling. Motivated by this, we present, for the first time, a novel, and unified impulse response modeling of underwater optical scattering channels based on the superposition of one impulsive component, and one dispersive component with two degrees of freedom. We provide analytical results for channel path loss, and channel impulse response (CIR) which are validated through Monte-Carlo simulations based on photon-tracing for clear ocean, coastal, and harbor waters. In order to provide a physical insight, the developed CIR is used to compute the root-mean-square (RMS) delay spread as a function of distance, and type of water, as well as to analyze in greater detail the impact of inter-symbol interference (ISI) on the data rate. These outcomes can be used for high-speed systems design, and optimization.
In this work, the ergodic capacity performance for multiple-input/single-output (MISO) free-space optical (FSO) communications system with equal gain combining (EGC) reception is analyzed over gamma-gamma and misalignment fading channels, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.). Novel and analytical closed-form ergodic capacity expression is obtained in terms of H-Fox function by using the well-known inequality between arithmetic and geometric mean of positive random variables (RV) in order to obtain an approximate closed-form expression of the distribution of the sum of M gamma-gamma with pointing errors variates. In addition, we present an asymptotic ergodic capacity expression at high signal-to-noise ratio (SNR) for the ergodic capacity of MISO FSO systems. It can be concluded that the use of MISO technique can significantly reduce the effect of the atmospheric turbulence as well as pointing errors and, hence, provide significant capacity gain over the direct path link (DL). The impact of pointing errors on the MISO FSO system is also analyzed, which only depends on the number of laser sources and pointing error parameters. Moreover, it can be also concluded that the ergodic capacity performance is dramatically reduced as a consequence of the severity of pointing error effects. Simulation results are further demonstrated to confirm the analytical results.
A thorough investigation of the impact of nonzero boresight pointing errors on the ergodic capacity of multiple-input/multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) reception under different turbulence models, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.) is addressed in this paper. Novel closed-form asymptotic expressions at high signal-to-noise ratio (SNR) for the ergodic capacity of MIMO FSO systems are derived when different geometric arrangements of the receive apertures at the receiver are considered in order to reduce the effect of nonzero inherent boresight displacement, which is inevitably present when more than one receive aperture is considered. As a result, the asymptotic ergodic capacity of MIMO FSO systems is evaluated over log-normal (LN), gamma-gamma (GG) and exponentiated Weibull (EW) atmospheric turbulence in order to study different turbulence conditions, different sizes of receive apertures as well as different aperture averaging conditions. It is concluded that the use of single-input/multiple-output (SIMO) and MIMO techniques can significantly increase the ergodic capacity respect to the direct path link when the inherent boresight displacement takes small values, i.e. when the spacing among receive apertures is not too big. The effect of nonzero additional boresight errors, which is due to the thermal expansion of the building, is evaluated in multiple-input/single-output (MISO) and single-input/single-output (SISO) FSO systems. Simulation results are further included to confirm the analytical results.
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